﻿// Copyright (c) 2010-2014 SharpDX - Alexandre Mutel
// 
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// 
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// -----------------------------------------------------------------------------
// Original code from SlimMath project. http://code.google.com/p/slimmath/
// Greetings to SlimDX Group. Original code published with the following license:
// -----------------------------------------------------------------------------
/*
* Copyright (c) 2007-2011 SlimDX Group
* 
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
* 
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
* 
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/

using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Serialization;

namespace Molten;

/// <summary>
/// Represents a plane in three dimensional space.
/// </summary>
[StructLayout(LayoutKind.Sequential, Pack = 4)]
[Serializable]
public struct Plane : IEquatable<Plane>, IFormattable
{
    /// <summary>
    /// The normal vector of the plane.
    /// </summary>
    [DataMember]
    public Vector3F Normal;

    /// <summary>
    /// The distance of the plane along its normal from the origin.
    /// </summary>
    [DataMember]
    public float D;

    /// <summary>
    /// Initializes a new instance of the <see cref="Plane"/> struct.
    /// </summary>
    /// <param name="value">The value that will be assigned to all components.</param>
    public Plane(float value)
    {
        Normal.X = Normal.Y = Normal.Z = D = value;
    }

    /// <summary>
    /// Initializes a new instance of the <see cref="Plane"/> struct.
    /// </summary>
    /// <param name="a">The X component of the normal.</param>
    /// <param name="b">The Y component of the normal.</param>
    /// <param name="c">The Z component of the normal.</param>
    /// <param name="d">The distance of the plane along its normal from the origin.</param>
    public Plane(float a, float b, float c, float d)
    {
        Normal.X = a;
        Normal.Y = b;
        Normal.Z = c;
        D = d;
    }

    /// <summary>
    /// Initializes a new instance of the <see cref="T:SharpDX.Plane" /> class.
    /// </summary>
    /// <param name="point">Any point that lies along the plane.</param>
    /// <param name="normal">The normal vector to the plane.</param>
    public Plane(Vector3F point, Vector3F normal)
    {
        this.Normal = normal;
        this.D = -Vector3F.Dot(normal, point);
    }

    /// <summary>
    /// Initializes a new instance of the <see cref="Plane"/> struct.
    /// </summary>
    /// <param name="value">The normal of the plane.</param>
    /// <param name="d">The distance of the plane along its normal from the origin</param>
    public Plane(Vector3F value, float d)
    {
        Normal = value;
        D = d;
    }

    /// <summary>
    /// Initializes a new instance of the <see cref="Plane"/> struct.
    /// </summary>
    /// <param name="point1">First point of a triangle defining the plane.</param>
    /// <param name="point2">Second point of a triangle defining the plane.</param>
    /// <param name="point3">Third point of a triangle defining the plane.</param>
    public Plane(Vector3F point1, Vector3F point2, Vector3F point3)
    {
        float x1 = point2.X - point1.X;
        float y1 = point2.Y - point1.Y;
        float z1 = point2.Z - point1.Z;
        float x2 = point3.X - point1.X;
        float y2 = point3.Y - point1.Y;
        float z2 = point3.Z - point1.Z;
        float yz = (y1 * z2) - (z1 * y2);
        float xz = (z1 * x2) - (x1 * z2);
        float xy = (x1 * y2) - (y1 * x2);
        float invPyth = 1.0f / float.Sqrt((yz * yz) + (xz * xz) + (xy * xy));

        Normal.X = yz * invPyth;
        Normal.Y = xz * invPyth;
        Normal.Z = xy * invPyth;
        D = -((Normal.X * point1.X) + (Normal.Y * point1.Y) + (Normal.Z * point1.Z));
    }

    /// <summary>
    /// Initializes a new instance of the <see cref="Plane"/> struct.
    /// </summary>
    /// <param name="values">The values to assign to the A, B, C, and D components of the plane. This must be an array with four elements.</param>
    /// <exception cref="ArgumentNullException">Thrown when <paramref name="values"/> is <c>null</c>.</exception>
    /// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="values"/> contains more or less than four elements.</exception>
    public Plane(float[] values)
    {
        if (values == null)
            throw new ArgumentNullException("values");
        if (values.Length != 4)
            throw new ArgumentOutOfRangeException("values", "There must be four and only four input values for Plane.");

        Normal.X = values[0];
        Normal.Y = values[1];
        Normal.Z = values[2];
        D = values[3];
    }

    /// <summary>
    /// Gets or sets the component at the specified index.
    /// </summary>
    /// <value>The value of the A, B, C, or D component, depending on the index.</value>
    /// <param name="index">The index of the component to access. Use 0 for the A component, 1 for the B component, 2 for the C component, and 3 for the D component.</param>
    /// <returns>The value of the component at the specified index.</returns>
    /// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index"/> is out of the range [0, 3].</exception>
    public float this[int index]
    {
        get
        {
            switch (index)
            {
                case 0: return Normal.X;
                case 1: return Normal.Y;
                case 2: return Normal.Z;
                case 3: return D;
            }

            throw new ArgumentOutOfRangeException("index", "Indices for Plane run from 0 to 3, inclusive.");
        }

        set
        {
            switch (index)
            {
                case 0: Normal.X = value; break;
                case 1: Normal.Y = value; break;
                case 2: Normal.Z = value; break;
                case 3: D = value; break;
                default: throw new ArgumentOutOfRangeException("index", "Indices for Plane run from 0 to 3, inclusive.");
            }
        }
    }

    /// <summary>
    /// Changes the coefficients of the normal vector of the plane to make it of unit length.
    /// </summary>
    public void Normalize()
    {
        float magnitude = 1.0f / float.Sqrt((Normal.X * Normal.X) + (Normal.Y * Normal.Y) + (Normal.Z * Normal.Z));

        Normal.X *= magnitude;
        Normal.Y *= magnitude;
        Normal.Z *= magnitude;
        D *= magnitude;
    }

    /// <summary>
    /// Creates an array containing the elements of the plane.
    /// </summary>
    /// <returns>A four-element array containing the components of the plane.</returns>
    public float[] ToArray()
    {
        return new float[] { Normal.X, Normal.Y, Normal.Z, D };
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a point.
    /// </summary>
    /// <param name="point">The point to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public PlaneIntersectionType Intersects(ref Vector3F point)
    {
        return CollisionHelper.PlaneIntersectsPoint(ref this, ref point);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="Ray"/>.
    /// </summary>
    /// <param name="ray">The ray to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public bool Intersects(ref Ray ray)
    {
        float distance;
        return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out distance);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="Ray"/>.
    /// </summary>
    /// <param name="ray">The ray to test.</param>
    /// <param name="distance">When the method completes, contains the distance of the intersection,
    /// or 0 if there was no intersection.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public bool Intersects(ref Ray ray, out float distance)
    {
        return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out distance);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="Ray"/>.
    /// </summary>
    /// <param name="ray">The ray to test.</param>
    /// <param name="point">When the method completes, contains the point of intersection,
    /// or <see cref="Vector3F.Zero"/> if there was no intersection.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public bool Intersects(ref Ray ray, out Vector3F point)
    {
        return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out point);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="Plane"/>.
    /// </summary>
    /// <param name="plane">The plane to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public bool Intersects(ref Plane plane)
    {
        return CollisionHelper.PlaneIntersectsPlane(ref this, ref plane);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="Plane"/>.
    /// </summary>
    /// <param name="plane">The plane to test.</param>
    /// <param name="line">When the method completes, contains the line of intersection
    /// as a <see cref="Ray"/>, or a zero ray if there was no intersection.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public bool Intersects(ref Plane plane, out Ray line)
    {
        return CollisionHelper.PlaneIntersectsPlane(ref this, ref plane, out line);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a triangle.
    /// </summary>
    /// <param name="vertex1">The first vertex of the triangle to test.</param>
    /// <param name="vertex2">The second vertex of the triangle to test.</param>
    /// <param name="vertex3">The third vertex of the triangle to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public PlaneIntersectionType Intersects(ref Vector3F vertex1, ref Vector3F vertex2, ref Vector3F vertex3)
    {
        return CollisionHelper.PlaneIntersectsTriangle(ref this, ref vertex1, ref vertex2, ref vertex3);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="BoundingBox"/>.
    /// </summary>
    /// <param name="box">The box to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public PlaneIntersectionType Intersects(ref BoundingBox box)
    {
        return CollisionHelper.PlaneIntersectsBox(ref this, ref box);
    }

    /// <summary>
    /// Determines if there is an intersection between the current object and a <see cref="BoundingSphere"/>.
    /// </summary>
    /// <param name="sphere">The sphere to test.</param>
    /// <returns>Whether the two objects intersected.</returns>
    public PlaneIntersectionType Intersects(ref BoundingSphere sphere)
    {
        return CollisionHelper.PlaneIntersectsSphere(ref this, ref sphere);
    }

    /// <summary>
    /// Builds a matrix that can be used to reflect vectors about a plane.
    /// </summary>
    /// <param name="plane">The plane for which the reflection occurs. This parameter is assumed to be normalized.</param>
    /// <param name="result">When the method completes, contains the reflection matrix.</param>
    public void Reflection(out Matrix4F result)
    {
        float x = this.Normal.X;
        float y = this.Normal.Y;
        float z = this.Normal.Z;
        float x2 = -2.0f * x;
        float y2 = -2.0f * y;
        float z2 = -2.0f * z;

        result.M11 = (x2 * x) + 1.0f;
        result.M12 = y2 * x;
        result.M13 = z2 * x;
        result.M14 = 0.0f;
        result.M21 = x2 * y;
        result.M22 = (y2 * y) + 1.0f;
        result.M23 = z2 * y;
        result.M24 = 0.0f;
        result.M31 = x2 * z;
        result.M32 = y2 * z;
        result.M33 = (z2 * z) + 1.0f;
        result.M34 = 0.0f;
        result.M41 = x2 * this.D;
        result.M42 = y2 * this.D;
        result.M43 = z2 * this.D;
        result.M44 = 1.0f;
    }

    /// <summary>
    /// Builds a matrix that can be used to reflect vectors about a plane.
    /// </summary>
    /// <returns>The reflection matrix.</returns>
    public Matrix4F Reflection()
    {
        Matrix4F result;
        Reflection(out result);
        return result;
    }

    /// <summary>
    /// Creates a matrix that flattens geometry into a shadow from this the plane onto which to project the geometry as a shadow. 
    /// This plane  is assumed to be normalized
    /// </summary>
    /// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
    /// W component is 1, the light is a point light.</param>
    /// <param name="result">When the method completes, contains the shadow matrix.</param>
    public void Shadow(ref Vector4F light, out Matrix4F result)
    {
        float dot = (this.Normal.X * light.X) + (this.Normal.Y * light.Y) + (this.Normal.Z * light.Z) + (this.D * light.W);
        float x = -this.Normal.X;
        float y = -this.Normal.Y;
        float z = -this.Normal.Z;
        float d = -this.D;

        result.M11 = (x * light.X) + dot;
        result.M21 = y * light.X;
        result.M31 = z * light.X;
        result.M41 = d * light.X;
        result.M12 = x * light.Y;
        result.M22 = (y * light.Y) + dot;
        result.M32 = z * light.Y;
        result.M42 = d * light.Y;
        result.M13 = x * light.Z;
        result.M23 = y * light.Z;
        result.M33 = (z * light.Z) + dot;
        result.M43 = d * light.Z;
        result.M14 = x * light.W;
        result.M24 = y * light.W;
        result.M34 = z * light.W;
        result.M44 = (d * light.W) + dot;
    }

    /// <summary>
    /// Creates a matrix that flattens geometry into a shadow from this the plane onto which to project the geometry as a shadow. 
    /// This plane  is assumed to be normalized
    /// </summary>
    /// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
    /// W component is 1, the light is a point light.</param>
    /// <returns>The shadow matrix.</returns>
    public Matrix4F Shadow(Vector4F light)
    {
        Matrix4F result;
        Shadow(ref light, out result);
        return result;
    }

    /// <summary>
    /// Builds a Matrix3x3 that can be used to reflect vectors about a plane for which the reflection occurs. 
    /// This plane is assumed to be normalized
    /// </summary>
    /// <param name="result">When the method completes, contains the reflection Matrix3x3.</param>
    public void Reflection(out Matrix3F result)
    {
        float x = this.Normal.X;
        float y = this.Normal.Y;
        float z = this.Normal.Z;
        float x2 = -2.0f * x;
        float y2 = -2.0f * y;
        float z2 = -2.0f * z;

        result.M11 = (x2 * x) + 1.0f;
        result.M12 = y2 * x;
        result.M13 = z2 * x;
        result.M21 = x2 * y;
        result.M22 = (y2 * y) + 1.0f;
        result.M23 = z2 * y;
        result.M31 = x2 * z;
        result.M32 = y2 * z;
        result.M33 = (z2 * z) + 1.0f;
    }

    /// <summary>
    /// Builds a Matrix3x3 that can be used to reflect vectors about a plane for which the reflection occurs. 
    /// This plane is assumed to be normalized
    /// </summary>
    /// <returns>The reflection Matrix3x3.</returns>
    public Matrix3F Reflection3x3()
    {
        Matrix3F result;
        Reflection(out result);
        return result;
    }

    /// <summary>
    /// Creates a Matrix3x3 that flattens geometry into a shadow.
    /// </summary>
    /// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
    /// W component is 1, the light is a point light.</param>
    /// <param name="plane">The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.</param>
    /// <param name="result">When the method completes, contains the shadow Matrix3x3.</param>
    public static void Shadow(ref Vector4F light, ref Plane plane, out Matrix3F result)
    {
        float dot = (plane.Normal.X * light.X) + (plane.Normal.Y * light.Y) + (plane.Normal.Z * light.Z) + (plane.D * light.W);
        float x = -plane.Normal.X;
        float y = -plane.Normal.Y;
        float z = -plane.Normal.Z;
        float d = -plane.D;

        result.M11 = (x * light.X) + dot;
        result.M21 = y * light.X;
        result.M31 = z * light.X;
        result.M12 = x * light.Y;
        result.M22 = (y * light.Y) + dot;
        result.M32 = z * light.Y;
        result.M13 = x * light.Z;
        result.M23 = y * light.Z;
        result.M33 = (z * light.Z) + dot;
    }

    /// <summary>
    /// Creates a Matrix3x3 that flattens geometry into a shadow.
    /// </summary>
    /// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
    /// W component is 1, the light is a point light.</param>
    /// <param name="plane">The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.</param>
    /// <returns>The shadow Matrix3x3.</returns>
    public static Matrix3F Shadow(Vector4F light, Plane plane)
    {
        Matrix3F result;
        Shadow(ref light, ref plane, out result);
        return result;
    }


    /// <summary>
    /// Scales the plane by the given scaling factor.
    /// </summary>
    /// <param name="value">The plane to scale.</param>
    /// <param name="scale">The amount by which to scale the plane.</param>
    /// <param name="result">When the method completes, contains the scaled plane.</param>
    public static void Multiply(ref Plane value, float scale, out Plane result)
    {
        result.Normal.X = value.Normal.X * scale;
        result.Normal.Y = value.Normal.Y * scale;
        result.Normal.Z = value.Normal.Z * scale;
        result.D = value.D * scale;
    }

    /// <summary>
    /// Scales the plane by the given scaling factor.
    /// </summary>
    /// <param name="value">The plane to scale.</param>
    /// <param name="scale">The amount by which to scale the plane.</param>
    /// <returns>The scaled plane.</returns>
    public static Plane Multiply(Plane value, float scale)
    {
        return new Plane(value.Normal.X * scale, value.Normal.Y * scale, value.Normal.Z * scale, value.D * scale);
    }

    /// <summary>
    /// Calculates the dot product of the specified vector and plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <param name="result">When the method completes, contains the dot product of the specified plane and vector.</param>
    public static void Dot(ref Plane left, ref Vector4F right, out float result)
    {
        result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + (left.D * right.W);
    }

    /// <summary>
    /// Calculates the dot product of the specified vector and plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <returns>The dot product of the specified plane and vector.</returns>
    public static float Dot(Plane left, Vector4F right)
    {
        return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + (left.D * right.W);
    }

    /// <summary>
    /// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <param name="result">When the method completes, contains the dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</param>
    public static void DotCoordinate(ref Plane left, ref Vector3F right, out float result)
    {
        result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + left.D;
    }

    /// <summary>
    /// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <returns>The dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</returns>
    public static float DotCoordinate(Plane left, Vector3F right)
    {
        return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + left.D;
    }

    /// <summary>
    /// Gets the dot product of the position offset from the plane along the plane's normal.
    /// </summary>
    /// <param name="v">Position to compute the dot product of.</param>
    /// <param name="dot">Dot product.</param>
    public void DotCoordinate(ref Vector3F v, out float dot)
    {
        dot = Normal.X * v.X + Normal.Y * v.Y + Normal.Z * v.Z + D;
    }

    /// <summary>
    /// Calculates the dot product of the specified vector and the normal of the plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <param name="result">When the method completes, contains the dot product of the specified vector and the normal of the plane.</param>
    public static void DotNormal(ref Plane left, ref Vector3F right, out float result)
    {
        result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z);
    }

    /// <summary>
    /// Calculates the dot product of the specified vector and the normal of the plane.
    /// </summary>
    /// <param name="left">The source plane.</param>
    /// <param name="right">The source vector.</param>
    /// <returns>The dot product of the specified vector and the normal of the plane.</returns>
    public static float DotNormal(Plane left, Vector3F right)
    {
        return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z);
    }

    /// <summary>
    /// Changes the coefficients of the normal vector of the plane to make it of unit length.
    /// </summary>
    /// <param name="plane">The source plane.</param>
    /// <param name="result">When the method completes, contains the normalized plane.</param>
    public static void Normalize(ref Plane plane, out Plane result)
    {
        float magnitude = 1.0f / float.Sqrt((plane.Normal.X * plane.Normal.X) + (plane.Normal.Y * plane.Normal.Y) + (plane.Normal.Z * plane.Normal.Z));

        result.Normal.X = plane.Normal.X * magnitude;
        result.Normal.Y = plane.Normal.Y * magnitude;
        result.Normal.Z = plane.Normal.Z * magnitude;
        result.D = plane.D * magnitude;
    }

    /// <summary>
    /// Changes the coefficients of the normal vector of the plane to make it of unit length.
    /// </summary>
    /// <param name="plane">The source plane.</param>
    /// <returns>The normalized plane.</returns>
    public static Plane Normalize(Plane plane)
    {
        float magnitude = 1.0f / float.Sqrt((plane.Normal.X * plane.Normal.X) + (plane.Normal.Y * plane.Normal.Y) + (plane.Normal.Z * plane.Normal.Z));
        return new Plane(plane.Normal.X * magnitude, plane.Normal.Y * magnitude, plane.Normal.Z * magnitude, plane.D * magnitude);
    }

    /// <summary>
    /// Transforms a normalized plane by a quaternion rotation.
    /// </summary>
    /// <param name="plane">The normalized source plane.</param>
    /// <param name="rotation">The quaternion rotation.</param>
    /// <param name="result">When the method completes, contains the transformed plane.</param>
    public static void Transform(ref Plane plane, ref QuaternionF rotation, out Plane result)
    {
        float x2 = rotation.X + rotation.X;
        float y2 = rotation.Y + rotation.Y;
        float z2 = rotation.Z + rotation.Z;
        float wx = rotation.W * x2;
        float wy = rotation.W * y2;
        float wz = rotation.W * z2;
        float xx = rotation.X * x2;
        float xy = rotation.X * y2;
        float xz = rotation.X * z2;
        float yy = rotation.Y * y2;
        float yz = rotation.Y * z2;
        float zz = rotation.Z * z2;

        float x = plane.Normal.X;
        float y = plane.Normal.Y;
        float z = plane.Normal.Z;

        result.Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
        result.Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
        result.Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
        result.D = plane.D;
    }

    /// <summary>
    /// Transforms a normalized plane by a quaternion rotation.
    /// </summary>
    /// <param name="plane">The normalized source plane.</param>
    /// <param name="rotation">The quaternion rotation.</param>
    /// <returns>The transformed plane.</returns>
    public static Plane Transform(Plane plane, QuaternionF rotation)
    {
        Plane result;
        float x2 = rotation.X + rotation.X;
        float y2 = rotation.Y + rotation.Y;
        float z2 = rotation.Z + rotation.Z;
        float wx = rotation.W * x2;
        float wy = rotation.W * y2;
        float wz = rotation.W * z2;
        float xx = rotation.X * x2;
        float xy = rotation.X * y2;
        float xz = rotation.X * z2;
        float yy = rotation.Y * y2;
        float yz = rotation.Y * z2;
        float zz = rotation.Z * z2;

        float x = plane.Normal.X;
        float y = plane.Normal.Y;
        float z = plane.Normal.Z;

        result.Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
        result.Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
        result.Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
        result.D = plane.D;

        return result;
    }

    /// <summary>
    /// Transforms an array of normalized planes by a quaternion rotation.
    /// </summary>
    /// <param name="planes">The array of normalized planes to transform.</param>
    /// <param name="rotation">The quaternion rotation.</param>
    /// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
    public static void Transform(Plane[] planes, ref QuaternionF rotation)
    {
        if (planes == null)
            throw new ArgumentNullException("planes");

        float x2 = rotation.X + rotation.X;
        float y2 = rotation.Y + rotation.Y;
        float z2 = rotation.Z + rotation.Z;
        float wx = rotation.W * x2;
        float wy = rotation.W * y2;
        float wz = rotation.W * z2;
        float xx = rotation.X * x2;
        float xy = rotation.X * y2;
        float xz = rotation.X * z2;
        float yy = rotation.Y * y2;
        float yz = rotation.Y * z2;
        float zz = rotation.Z * z2;

        for (int i = 0; i < planes.Length; ++i)
        {
            float x = planes[i].Normal.X;
            float y = planes[i].Normal.Y;
            float z = planes[i].Normal.Z;

            /*
             * Note:
             * Factor common arithmetic out of loop.
            */
            planes[i].Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
            planes[i].Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
            planes[i].Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
        }
    }

    /// <summary>
    /// Transforms a normalized plane by a matrix.
    /// </summary>
    /// <param name="plane">The normalized source plane.</param>
    /// <param name="transformation">The transformation matrix.</param>
    /// <param name="result">When the method completes, contains the transformed plane.</param>
    public static void Transform(ref Plane plane, ref Matrix4F transformation, out Plane result)
    {
        float x = plane.Normal.X;
        float y = plane.Normal.Y;
        float z = plane.Normal.Z;
        float d = plane.D;

        Matrix4F inverse;
        Matrix4F.Invert(ref transformation, out inverse);

        result.Normal.X = (((x * inverse.M11) + (y * inverse.M12)) + (z * inverse.M13)) + (d * inverse.M14);
        result.Normal.Y = (((x * inverse.M21) + (y * inverse.M22)) + (z * inverse.M23)) + (d * inverse.M24);
        result.Normal.Z = (((x * inverse.M31) + (y * inverse.M32)) + (z * inverse.M33)) + (d * inverse.M34);
        result.D = (((x * inverse.M41) + (y * inverse.M42)) + (z * inverse.M43)) + (d * inverse.M44);
    }

    /// <summary>
    /// Transforms a normalized plane by a matrix.
    /// </summary>
    /// <param name="plane">The normalized source plane.</param>
    /// <param name="transformation">The transformation matrix.</param>
    /// <returns>When the method completes, contains the transformed plane.</returns>
    public static Plane Transform(Plane plane, Matrix4F transformation)
    {
        Plane result;
        float x = plane.Normal.X;
        float y = plane.Normal.Y;
        float z = plane.Normal.Z;
        float d = plane.D;

        transformation.Invert();
        result.Normal.X = (((x * transformation.M11) + (y * transformation.M12)) + (z * transformation.M13)) + (d * transformation.M14);
        result.Normal.Y = (((x * transformation.M21) + (y * transformation.M22)) + (z * transformation.M23)) + (d * transformation.M24);
        result.Normal.Z = (((x * transformation.M31) + (y * transformation.M32)) + (z * transformation.M33)) + (d * transformation.M34);
        result.D = (((x * transformation.M41) + (y * transformation.M42)) + (z * transformation.M43)) + (d * transformation.M44);

        return result;
    }

    /// <summary>
    /// Transforms an array of normalized planes by a matrix.
    /// </summary>
    /// <param name="planes">The array of normalized planes to transform.</param>
    /// <param name="transformation">The transformation matrix.</param>
    /// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
    public static void Transform(Plane[] planes, ref Matrix4F transformation)
    {
        if (planes == null)
            throw new ArgumentNullException("planes");

        Matrix4F inverse;
        Matrix4F.Invert(ref transformation, out inverse);

        for (int i = 0; i < planes.Length; ++i)
        {
            Transform(ref planes[i], ref transformation, out planes[i]);
        }
    }

    /// <summary>
    /// Scales a plane by the given value.
    /// </summary>
    /// <param name="scale">The amount by which to scale the plane.</param>
    /// <param name="plane">The plane to scale.</param>
    /// <returns>The scaled plane.</returns>
    public static Plane operator *(float scale, Plane plane)
    {
        return new Plane(plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale);
    }

    /// <summary>
    /// Scales a plane by the given value.
    /// </summary>
    /// <param name="plane">The plane to scale.</param>
    /// <param name="scale">The amount by which to scale the plane.</param>
    /// <returns>The scaled plane.</returns>
    public static Plane operator *(Plane plane, float scale)
    {
        return new Plane(plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale);
    }

    /// <summary>
    /// Tests for equality between two objects.
    /// </summary>
    /// <param name="left">The first value to compare.</param>
    /// <param name="right">The second value to compare.</param>
    /// <returns><c>true</c> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <c>false</c>.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool operator ==(Plane left, Plane right)
    {
        return left.Equals(ref right);
    }

    /// <summary>
    /// Tests for inequality between two objects.
    /// </summary>
    /// <param name="left">The first value to compare.</param>
    /// <param name="right">The second value to compare.</param>
    /// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool operator !=(Plane left, Plane right)
    {
        return !left.Equals(ref right);
    }

    /// <summary>
    /// Returns a <see cref="System.String"/> that represents this instance.
    /// </summary>
    /// <returns>
    /// A <see cref="System.String"/> that represents this instance.
    /// </returns>
    public override string ToString()
    {
        return string.Format(CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D);
    }

    /// <summary>
    /// Returns a <see cref="System.String"/> that represents this instance.
    /// </summary>
    /// <param name="format">The format.</param>
    /// <returns>
    /// A <see cref="System.String"/> that represents this instance.
    /// </returns>
    public string ToString(string format)
    {
        return string.Format(CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString(format, CultureInfo.CurrentCulture),
            Normal.Y.ToString(format, CultureInfo.CurrentCulture), Normal.Z.ToString(format, CultureInfo.CurrentCulture), D.ToString(format, CultureInfo.CurrentCulture));
    }

    /// <summary>
    /// Returns a <see cref="System.String"/> that represents this instance.
    /// </summary>
    /// <param name="formatProvider">The format provider.</param>
    /// <returns>
    /// A <see cref="System.String"/> that represents this instance.
    /// </returns>
    public string ToString(IFormatProvider formatProvider)
    {
        return string.Format(formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D);
    }

    /// <summary>
    /// Returns a <see cref="System.String"/> that represents this instance.
    /// </summary>
    /// <param name="format">The format.</param>
    /// <param name="formatProvider">The format provider.</param>
    /// <returns>
    /// A <see cref="System.String"/> that represents this instance.
    /// </returns>
    public string ToString(string format, IFormatProvider formatProvider)
    {
        return string.Format(formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString(format, formatProvider),
            Normal.Y.ToString(format, formatProvider), Normal.Z.ToString(format, formatProvider), D.ToString(format, formatProvider));
    }

    /// <summary>
    /// Returns a hash code for this instance.
    /// </summary>
    /// <returns>
    /// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table. 
    /// </returns>
    public override int GetHashCode()
    {
        unchecked
        {
            return (Normal.GetHashCode() * 397) ^ D.GetHashCode();
        }
    }

    /// <summary>
    /// Determines whether the specified <see cref="Vector4F"/> is equal to this instance.
    /// </summary>
    /// <param name="value">The <see cref="Vector4F"/> to compare with this instance.</param>
    /// <returns>
    /// <c>true</c> if the specified <see cref="Vector4F"/> is equal to this instance; otherwise, <c>false</c>.
    /// </returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public bool Equals(ref Plane value)
    {
        return Normal == value.Normal && D == value.D;
    }

    /// <summary>
    /// Determines whether the specified <see cref="Vector4F"/> is equal to this instance.
    /// </summary>
    /// <param name="value">The <see cref="Vector4F"/> to compare with this instance.</param>
    /// <returns>
    /// <c>true</c> if the specified <see cref="Vector4F"/> is equal to this instance; otherwise, <c>false</c>.
    /// </returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public bool Equals(Plane value)
    {
        return Equals(ref value);
    }

    /// <summary>
    /// Determines whether the specified <see cref="System.Object"/> is equal to this instance.
    /// </summary>
    /// <param name="value">The <see cref="System.Object"/> to compare with this instance.</param>
    /// <returns>
    /// <c>true</c> if the specified <see cref="System.Object"/> is equal to this instance; otherwise, <c>false</c>.
    /// </returns>
    public override bool Equals(object value)
    {
        if (!(value is Plane))
            return false;

        var strongValue = (Plane)value;
        return Equals(ref strongValue);
    }
}
